Dadashov had the first chance for the hosts in the 25th minute after being found by Rauf Aliyev, but his shot curled wide of the post. Aliyev then called Roy Carroll into action when his header was well saved by the goalkeeper.
Martin Paterson almost gave the visitors the lead before the break, but he could only divert his close-range effort wide of the post.
The hosts went close three minutes into the second half when Dadashov fired a strike wide of the post after being picked out by a good cross from Shukurov.
Dadashov broke the deadlock after 58 minutes when he converted Aliyev's cross from close range following a fine team move.
Northern Ireland struggled to break down a stubborn Azerbaijan defence following the goal, with Jamie Ward's effort being blocked by Shukurov.
Paterson came closest to levelling the scores in the 87th minute when his powerful drive came back out off the post.
Jonny Evans was sent off in injury time for kicking out at Aliyev and Shukurov converted the resulting free kick from 20 yards to seal victory for the hosts.